Optimization of steady wall temperature for disturbance control

We present a theory for computing the optimal steady wall temperature distribution to suppress the growth of convectively unstable disturbances in compressible boundary layer flows on flat plates. A gradient based iterative procedure is used to minimize an objective function measuring the disturbance kinetic energy. The gradient of interest is obtained from the solution of the adjoint of the boundary layer and parabolized stability equations, which are derived using a Lagrange multiple technique. The study includes a comparison between the cases of minimizing the terminal, and an integrated value of the disturbance kinetic energy for different freestream Mach number and control magnitudes. A comparison is also made for the cases of zero and non-zero wall heat transfer outside the control domain.